Advances in Operator Theory

Fixed point results for a new mapping related to mean nonexpansive mappings

Torrey M Gallagher

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Mean nonexpansive mappings were first introduced in 2007 by Goebel and Japón Pineda and advances have been made by several authors toward understanding their fixed point properties in various contexts. For any given mean nonexpansive mapping of a Banach space, many of the positive results have been derived from knowing that a certain average of some iterates of the mapping is nonexpansive. However, nothing is known about the properties of a mean nonexpansive mapping which has been averaged with the identity. In this paper we prove some fixed point results for a mean nonexpansive mapping which has been composed with a certain average of itself and the identity and we use this study to draw connections to the original mapping.

Article information

Adv. Oper. Theory, Volume 2, Number 1 (2017), 1-16.

Received: 12 October 2016
Accepted: 20 December 2016
First available in Project Euclid: 4 December 2017

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 47H10: Fixed-point theorems [See also 37C25, 54H25, 55M20, 58C30]
Secondary: 47H14: Perturbations of nonlinear operators [See also 47A55, 58J37, 70H09, 70K60, 81Q15]

mean nonexpansive fixed point approximate fixed point sequence nonexpansive nonlinear operator


Gallagher, Torrey M. Fixed point results for a new mapping related to mean nonexpansive mappings. Adv. Oper. Theory 2 (2017), no. 1, 1--16. doi:10.22034/aot.1610.1029.

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  • F. E. Browder, Fixed-point theorems for noncompact mappings in Hilbert space, Proc. Nat. Acad. Sci. U.S.A. 53 (1965), 1272–1276.
  • F. E. Browder, Nonexpansive nonlinear operators in a Banach space, Proc. Nat. Acad. Sci. U.S.A. 54 (1965), 1041–1044.
  • J. A. Clarkson, Uniformly convex spaces, Trans. Amer. Math. Soc. 40 (1936), no. 3, 396-414.
  • T. M. Gallagher, The demiclosedness principle for mean nonexpansive mappings, J. Math. Anal. Appl. 439 (2016), no. 2, 832–842.
  • V. P. García and Ł. Piasecki, On mean nonexpansive mappings and the Lifshitz constant, J. Math. Anal. Appl. 396 (2012), no. 2, 448–454.
  • K. Goebel and M. Japon Pineda, A new type of nonexpansiveness, Proceedings of 8-th International Conference on Fixed Point Theory and Applications, Chiang Mai, 2007.
  • K. Goebel and B. Sims, Mean lipschitzian mappings, Nonlinear analysis and optimization I. Nonlinear analysis, 157–167, Contemp. Math., 513, Amer. Math. Soc., Providence, RI, 2010.
  • K. Goebel and W. A. Kirk, Topics in metric fixed point theory, Cambridge Studies in Advanced Mathematics, 28. Cambridge University Press, Cambridge, 1990.
  • D. G öhde, Zum prinzip der kontraktiven abbildung (German), Math. Nachr. 30 (1965), 251–258.
  • W. A. Kirk, A fixed point theorem for mappings which do not increase distances, Amer. Math. Monthly 72 (1965), 1004-1006.
  • W. A. Kirk and B. Sims (eds), Handbook of Metric Fixed Point Theory, Kluwer Academic Publishers, Dordrecht, 2001.
  • Ł. Piasecki, Classification of Lipschitz Mappings, Pure and Applied Mathematics (Boca Raton), 307. CRC Press, Boca Raton, FL, 2014.